Transfer Principle wrote: > On Nov 6, 6:00 pm, Brian Chandler <imaginator...@despammed.com> wrote: > > Daryl McCullough wrote: > > > I don't think that's right at all. It doesn't have anything > > > to do with 6 being special. > > Never mind about being special, I'm completely baffled by the concept > > of the "object" [!?] 6. What on earth does it mean for it to "exist"? > > It seems to me that 6 only exists in the (incontrovertible) sense that > > the Judaeo-Christian God "exists"
> Exactly! Of course, most people in the world believe in the existence > of the > number six -- even more than believe in the Judaeo-Christian God --
Not exactly. You seem to have misunderstood my comment. In one sense 6, God, the tooth fairy, Harry Potter, and the harp part from the intermezzo of Cavalleria Rusticana all exist, or we couldn't talk about them. Shakespeare's play "Tony gets to Infinity", Llanfrwyberimych the Welsh god of lardies, and the integer square root of 7 do not exist (none of them has a Wikipedia entry, which clinches it).
There is a different notion of "Existence", which I'll capitalise: all sane people understand that Harry Potter is fictional, and doesn't Exist in this sense; probably almost everyone agrees that the tooth fairy doesn't Exist; there are differences of opinion whether God Exists, and so on. My point was that there is no coherent sense in which 6 could be said to Exist, which is why posters who go on about infinity "existing" or "not existing" always turn out to be cranks.
More simply, mathematics is fiction, just like poetry or music (which is why the analogy of regarding it as a "language" is at least as valid as regarding music as a language). Just as a poem comes into existence by the poet thinking of it, so do ineffable cardinals, and the rest of it, and so would Big'un if its creator managed to provide a coherent definition of it.
> people are more divided on the existence of certain natural numbers > that > are much, much larger than six. Try 10^600 -- there are active threads > at > sci.math that question the existence of numbers larger than 10^600.
Yes, and I think that these claims are totally loopy. Exactly like people having arguments about whether Harry Potter _actually_ has astigmatism. If JK Rowling churns out another one, in which she reveals that HP has no astigmatism whatsoever, then that's the answer.